Gauss Seidel Method Looping error ( Index exceeds the number of array elements (1). in LINE 54) V2n

MVA_Base = 100; %base MVA
V1 = 1.0;      %fixed voltage
V2o = 1.0;     %fixed voltage
V3o = 1.0;     %gauss voltage
P2 = 0.6;      % given active power on bus 2
Q1 = 0;        % reactive power on bus 1
Q2 = 0;        % reactive power on bus 2
P3 = -0.8;      % given active power on bus 3
Q3 = -0.6;     % reactive power on bus 3
X12 = 0.4;     % reactance between bus 1 & 2
X13 = 0.4;     % reactance between bus 1 & 3
X23 = 0.3;     % reactance between bus 2 & 3
 
% Ybus 
Y11 = (1/(1i*X12)) + (1/(1i*X13));
Y12 = -1/(1i*X12);
Y13 = -1/(1i*X13);
Y21 = -1/(1i*X12);
Y22 = (1/(1i*X12)) + (1/(1i*X23));
Y23 = -1/(1i*X23);
Y31 = -1/(1i*X13);
Y32 = -1/(1i*X23);
Y33 = (1/(1i*X13)) + (1/(1i*X23));
 YB = [ Y11 Y12 Y13;
          Y21 Y22 Y23;
          Y31 Y32 Y33];
 
n=0;         % Number of Iteration
 
type = [1 2 3]; % Bus Type: 1. Slack Bus    2. PV Bus    3.PQ Bus  
V = [ V1 V2o V3o];
Q = [ Q1 Q2 Q3];
Vprev = V ;
Qprev = Q2;
P=P2-P3;
Q=Q2-Q3;
Vmagfixed = 1.0;
tolerance=1;
nbus = 3;      % total number of buses.


while (tolerance > 0.00001)
   for i = 2:nbus
    
     sigYV = 0;
        
        for k = 1:nbus
           if i~=k
                sigYV = sigYV + YB(i,k)* V(k);    
            end
        end
        if type(i) == 2    
            Q2n = -imag(conj(V2o)*(sigYV + YB(i,i)*V2o)); % Computing Qi for PV bus
        V2n = (1/YB(i,i))*((P(i)-1i*Q2n)/conj(V(i))-sigYV); % Compute Bus Voltage.
        end  
        if type(i) == 3   
        V3n = (1/YB(i,i))*((P(i)-1i*Q(i))/conj(V(i)) - sigYV); % Compute Bus Voltage.
        end  
                if type(i) == 2 
            V2n = pol2cart (abs(Vmagfixed), angle(V2n)*180/pi);
                end
    end
    
    n = n + 1;      % Increment iteration count.
   DeltaV2 = abs(V2n-V2o);
   DeltaV3 = abs(V3n-V3o);
   DeltaQ2 = abs(Q2n-Q2);
   tolerance = max(DeltaV2,DeltaV3,DeltaQ2);
   
    if tolerance <=0.00001

     break;
    else
    V2o = V2n;
    V3o = V3n;
    end 
end

Iteration;
V;
 
%apparent power of line 
S12=(conj(V1)*V1*Y12)-(conj(V1)*V2*Y12);
S21=(conj(V2)*V2*Y21)-(conj(V2)*V1*Y21);
S23=(conj(V2)*V2*Y23)-(conj(V2)*V3*Y23);
S32=(conj(V3)*V3*Y32)-(conj(V3)*V2*Y32);
S31=(conj(V3)*V3*Y31)-(conj(V3)*V1*Y31);
S13=(conj(V1)*V1*Y13)-(conj(V1)*V3*Y13);
 
%apparent power on buses
S1=S12+S13;
S2=S23+S21;
S3=S31+S32;

[Walter Roberson]

        V2n = (1/YB(i,i))*((P(i)-1i*Q2n)/conj(V(i))-sigYV); % Compute Bus Voltage.

You initilized P as the difference between two scalars, so it is a scalar.

You index P at i, so when i is more than 1 you have a problem.

You never assign into further P locations, so your P would have to have nbus or more elements.

[Parth Soni]

added following 2 lines in program but getting same error for same line.

P= [P1 P2 P3];

P1 = 0;

Answer 1

[Shishir Reddy]

Hi Parth

The error you are encountering occurs at the following line in your Gauss-Seidel loop.

V2n = (1/YB(i,i))*((P(i)-1i*Q2n)/conj(V(i))-sigYV);

The root cause of this issue is that you have defined ‘P’ and ‘Q’ as scalars earlier in your code.

P = P2 - P3;
Q = Q2 - Q3;

This overwrites P and Q as single numbers (1-element arrays), which causes an indexing error when you later try to access P(i) or Q(i) inside the loop, especially when i = 2 or 3.

To fix this, ’P’ and ‘Q’ have to be vectors with size of nbus, which is 3 in this case.

P = [0, P2, P3];
Q = [0, Q2, Q3];

It is important to make sure that you initialize these values before the Gauss-Seidel loop.

Also, you have another issue with the 'max' function. The following line in the code will throw an error because 'max' only accepts one or two inputs.

max(DeltaV2, DeltaV3, DeltaQ2)

The values can be wraped in an array like this:

tolerance = max([DeltaV2, DeltaV3, DeltaQ2]);

These two changes should resolve the runtime errors in your Gauss-Seidel implementation.

I hope this helps.